Inertia Tensor and Center of Gravity Measurement for Engines and Other Automotive Components
Published April 2, 2019 by SAE International in United States
Downloadable datasets for this paper availableAnnotation of this paper is available
A machine has been developed to measure the complete inertia matrix; mass, center of gravity (CG) location, and all moments and products of inertia. Among other things these quantities are useful in studying engine vibrations, calculation of the torque roll axis, and in the placement of engine mounts. While the machine was developed primarily for engines it can be used for other objects of similar size and weight, and even smaller objects such as tires and wheels/rims.
A key feature of the device is that the object, once placed on the test table, is never reoriented during the test cycle. This reduces the testing time to an hour or less, with the setup time being a few minutes to a few hours depending on the complexity of the shape of the object. Other inertia test methods can require up to five reorientations, separate CG measurement, and up to several days for a complete test.
The device uses a system of pivots, springs, and three sensors to get the three moments and three products of inertia, plus the CG location. Object mass is measured separately on a scale. A stable pendulum arrangement is used to get the CG location, two moments and one product of inertia. A rotating plate with springs is used to get one moment of inertia, and a load cell is used to get two products of inertia. For typical passenger-vehicle engine-size objects accuracy is on the order of 2.5 mm for CG, 1% for moments of inertia, and 2% of the smallest moment for products of inertia.
The three sensors used are an inclinometer, a load cell, and a rotary encoder. Custom software is used to record the measurements from the sensors. The software performs all calculations, guides the user through the test sequence, and checks for possible testing errors.
CitationAndreatta, D., Heydinger, G., Zagorski, S., and Guenther, D., "Inertia Tensor and Center of Gravity Measurement for Engines and Other Automotive Components," SAE Technical Paper 2019-01-0701, 2019, https://doi.org/10.4271/2019-01-0701.
Data Sets - Support Documents
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